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Linear and Nonlinear Inverse Problems with Practical Applications
TLDR
Inverse problems arise in practical applications whenever there is a need to interpret indirect measurements. Expand
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Discretization-invariant Bayesian inversion and Besov space priors
Bayesian solution of an inverse problem for indirect measurement $M = AU + {\mathcal{E}}$ is considered, where $U$ is a function on a domain of $R^d$. Here $A$ is a smoothing linear operator and $Expand
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An implementation of the reconstruction algorithm of A Nachman for the 2 D inverse conductivity problem
The 2D inverse conductivity problem requires one to determine the unknown electrical conductivity distribution inside a bounded domain ⊂ R from knowledge of the Dirichletto-Neumann map. The problemExpand
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Can one use total variation prior for edge-preserving Bayesian inversion?
Estimation of non-discrete physical quantities from indirect linear measurements is considered. Bayesian solution of such an inverse problem involves discretizing the problem and expressing availableExpand
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REGULARIZED D-BAR METHOD FOR THE INVERSE CONDUCTIVITY PROBLEM
A strategy for regularizing the inversion procedure for the two-dimensional D-bar reconstruction algorithm based on the global uniqueness proof of Nachman [Ann. Math. 143 (1996)] for the ill-posedExpand
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Numerical solution method for the dbar-equation in the plane
A fast method for solving ∂--equations of the form ∂-v = Tv- is presented, where v and T are complex-valued functions of two real variables. The multigrid method of Vainikko [Int. Soc. Anal. Appl.Expand
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D-Bar Method for Electrical Impedance Tomography with Discontinuous Conductivities
TLDR
The effects of truncating the (approximate) scattering transform in the D‐bar reconstruction method for two‐dimensional electrical impedance tomography are studied. Expand
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Mapping Properties of the Nonlinear Fourier Transform in Dimension Two
A class of compactly supported Schrödinger potentials in dimension two is given for which the inverse scattering method related to the Novikov–Veselov evolution equation is well-defined. There is noExpand
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Reconstructions of chest phantoms by the D-bar method for electrical impedance tomography
TLDR
The problem this paper addresses is how to use the two-dimensional D-bar method for electrical impedance tomography with experimental data collected on finitely many electrodes covering a portion of the boundary of a body. Expand
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Direct Reconstructions of Conductivities from Boundary Measurements
TLDR
The problem of reconstructing an unknown electric conductivity from boundary measurements has applications in medical imaging, geophysics, and nondestructive testing. Expand
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